Functional Equations in Mathematical Analysis

The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research.

The present reprint provides some theoretical results (and their applications) in the fields of mathematical analysis and functional analysis, in which the concept of symmetry plays an essential role. More specifically, various problems are investigated in areas, such as: optimization problems, polynomial approximation on unbounded subsets, moment problems, variational inequalities, evolutionary problems, dynamical systems, generalized convexity, partial differential equations, and special spaces of self-adjoint operators. With various examples and applications to complement and substantiate the mathematical developments, the present reprint is a valuable guide for researchers, engineers, and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science, and economics.

by Yeol Je Cho (Author), Choonkil Park (Author), Themistocles M. Rassias (Author), Reza Saadati (Author)